Pavel Surynek

A novel approach to path planning for multiple robots in bi-connected graphs

This paper addresses a problem of path planning for multiple robots. An abstraction where the environment for robots is modeled as an undirected graph with robots placed in its vertices is used (this abstraction is also known as the problem of pebble motion on graphs). A class of the problem with bi-connected graph and at least two unoccupied vertices is defined. A novel polynomial-time solution algorithm for this class of problem is proposed. It is shown in the paper that the new algorithm significantly outperforms the existing state-of-the-art techniques applicable to the problem. Moreover, the performed experimental evaluation indicates that the new algorithm scales up well which make it suitable for practical problem solving.

Towards optimal cooperative path planning in hard setups through satisfiability solving

A novel approach to cooperative path-planning is presented. A SAT solver is used not to solve the whole instance but for optimizing the makespan of a sub-optimal solution. This approach is trying to exploit the ability of stateof- the-art SAT solvers to give a solution to relatively small instance quickly. A sub-optimal solution to the instance is obtained by some existent method first. It is then submitted to the optimization process which decomposes it into small subsequences for which optimal solutions are found by a SAT solver. The new shorter solution is subsequently obtained as concatenation of optimal subsolutions. The process is iterated until a fixed point is reached. This is the first method to produce near optimal solutions for densely populated environments; it can be also applied to domain-independent planning supposed that suboptimal planner is available.

An Application of Pebble Motion on Graphs to Abstract Multi-robot Path Planning

An abstraction of a problem of rearranging group of mobile robots is addressed in this paper (the problem of multi-robot path planning). The robots are moving in an environment in which they must avoid obstacles and each other. An abstraction where the environment is modeled as an undirected graph is adopted throughout this work. A case when the graph modeling the environment is bi-connected is particularly studied. This paper puts into a relation the well known problems of moving pebbles on graphs (sliding box puzzles) with problems of multi-robot path planning. Theoretical results gained for problems of pebble motion on graphs are utilized for the development of algorithms for multi-robot path planning. As the opti-mization variant of both problems (a shortest solution is required) is known to be computationally hard (NP-hard), we concentrate on construction of sub-optimal solving procedures. However, the quality of solution is still an objective. Therefore a process of composition of a sub-optimal solution of the problem (a plan) of the pre-calculated optimal plans for the sub-problems (macros) is suggested. The plan composition using macros was inte-grated into two existing sub-optimal solving algorithms. In both cases, substantial improvements of the quality of resulting plans were achieved in comparison to the origi-nal algorithms. The no less important result is that one of the existing algorithms was generalized by integrating macros for larger class of problems of multi-robot path planning.

SOLVING ABSTRACT COOPERATIVE PATH-FINDING IN DENSELY POPULATED ENVIRONMENTS

The problem of cooperative path‐finding is addressed in this work. A set of agents moving in a certain environment is given. Each agent needs to reach a given goal location. The task is to find spatial temporal paths for agents such that they eventually reach their goals by following these paths without colliding with each other. An abstraction where the environment is modeled as an undirected graph is adopted—vertices represent locations and edges represent passable regions. Agents are modeled as elements placed in the vertices while at most one agent can be located in a vertex at a time. At least one vertex remains unoccupied to allow agents to move. An agent can move into unoccupied neighboring vertex or into a vertex being currently vacated if a certain additional condition is satisfied. Two novel scalable algorithms for solving cooperative path‐finding in bi‐connected graphs are presented. Both algorithms target environments that are densely populated by agents. A theoretical and experimental evaluation shows that the suggested algorithms represent a viable alternative to search based techniques as well as to techniques employing permutation groups on the studied class of the problem.

Solving difficult SAT instances using greedy clique decomposition

We are dealing with solving difficult SAT instances in this paper. We propose a method for preprocessing SAT instances (CNF formulas) by using consistency techniques known from constraint programming methodology and by using our own consistency technique based on clique decomposition of a graph representing conflicts in the input formula. If the clique decomposition is of a good quality (cliques are appropriately large) it then allows us to make a strong reasoning over the SAT instance, which can in some cases even decide the satisfiability of the SAT instance without search. We implemented our preprocessing method in C++ and compared it with several state-of-the-art SAT solvers on selected difficult SAT instances. The result was a speedup in the order of magnitude compared to the tested SAT solvers.

Compact Representations of Cooperative Path-Finding as SAT Based on Matchings in Bipartite Graphs

This paper addresses make span optimal solving of cooperative path-finding problem (CPF) by translating it to propositional satisfiability (SAT). The task is to relocate set of agents to given goal positions so that they do not collide with each other. A novel SAT encoding of CPF is suggested. The novel encoding uses the concept of matching in a bipartite graph to separate spatial constraint of CPF from consideration of individual agents. The separation allowed reducing the size of encoding significantly. The conducted experimental evaluation shown that novel encoding can be solved faster than existing encodings for CPF and also that the SAT based methods dominates over A* based methods in environment densely occupied by agents.

On Propositional Encodings of Cooperative Path-Finding

The approach to solving cooperative-path finding (CPF) as propositional satisfiability (SAT) is revisited in this paper. An alternative encoding that exploits multi-valued state variables representing locations where a given agent resides is suggested. This encoding employs the ALL-DIFFERENT constraint to model the requirement that agents must not collide with each other. The use of suggested state variables also allowed us to incorporate certain heuristic reasoning to reduce the size of the propositional encoding of the problem. We show that our new domain-dependent encoding enables finding of optimal or near optimal solutions to CPFs in certain hard set-ups where A*-based techniques such as WHCA* fail to do so. Our finding is also that the ALL-DIFFERENT encoding can be solved faster than the existent encoding.

Encoding HTN planning as a Dynamic CSP

Constraint satisfaction methodology has proven to be a successful technique for solving variety of combinatorial and optimization problems. Despite this fact, it was exploited very little in the planning domain. In particular hierarchical task network planning (HTN) [2] seems to be suitable for use of constraint programming. The formulation of HTN planning problem involves a lot of structural information which can be used to prune the search space. Encoding of this structural information by means of constraint programming would provide an effective way for such pruning during the search for solution. This work is supported by the Czech Science Foundation under the contract 201/04/1102.

Modelling Alternatives in Temporal Networks

Temporal networks play an important role in solving planning problems and they are also used, though not as frequently, when solving scheduling problems. In this paper we propose an extension of temporal networks by parallel and alternative branching. This extension supports modelling of alternative paths in the network; in particular, it is motivated by modelling alternative process routes in manufacturing scheduling. We show that deciding which nodes can be consistently included in this extended temporal network is an NP-complete problem. To simplify solving this problem, we propose a pre-processing step whose goal is to identify classes of equivalent nodes. The ideas are presented using precedence networks, but we also show how they can be extended to simple temporal networks

Mutex reasoning in cooperative path finding modeled as propositional satisfiability

This paper addresses a problem of cooperative path finding (CPF) where the task is to find paths for agents of a group of agents. Each agent is given a starting and a goal position and its task is to reach the goal from the given start. When following the paths, agents must not collide with each other and must avoid obstacles. It is suggested to augment propositional encodings of CPF with a so called mutex reasoning. Mutex reasoning is trying to rule out unreachable situations to reduce the size of the search space. It is checked whether a given pair of locations is reachable by a given pair of agents cooperatively. If not occurrence of the pair of agents in the pair of vertices is forbidden. The performed experimental evaluation showed that mutex reasoning improves existent encodings by 2 to 5 times in terms of solving runtime when makespan optimal solutions are searched.